Performance Comparison of MIMO Systems over AWGN and Rician Channels with Zero Forcing Receivers

7/29/2019 Performance Comparison of MIMO Systems over AWGN and Rician Channels with Zero Forcing Receivers

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International Journal of Wireless & Mobile Networks (IJWMN) Vol. 5, No. 1, February 2013

DOI : 10.5121/ijwmn.2013.5106 73

Performance Comparison of MIMO Systems overAWGN and Rician Channels with Zero Forcing

Receivers

Navjot Kaur and Lavish Kansal

Lovely Professional University, Phagwara,E-mails: [email protected], [email protected]

Abstract

Multiple-Input Multiple-Output (MIMO) systems have been emerged as a technical breakthrough for

high-data-rate wireless transmission. The performance of MIMO system can be improved by using

different antenna selection so as to provide spatial diversity. In this paper, the performance of MIMO

system over AWGN (Additive White Gaussian Noise) and Rician fading channels with ZF receiver isanalyzed using different antenna configurations. The bit error rate performance characteristics of Zero-

Forcing (ZF) receiver is studied for M-PSK (M-ary Phase Shift Keying) modulation technique using

AWGN and Rician channels for the analysis purpose and their effect on BER (Bit Error Rate) have been

presented.

Keywords MIMO, spatial diversity, AWGN, Rician, fading, ZF, antenna, BER, M-PSK.

I.INTRODUCTIONMIMO systems make use of multiple antennas at the transmitter and receiver so as to increase

the data rates by means of spatial diversity. So MIMO systems are well-known in wireless

communications for high data rates. [1] The capacity of wireless systems can be increased by

varying the number of antennas.

The two primary reasons for using wireless communication over wired communication:

First is multi-path fading i.e. the variation of the signal strengths due to the variousobstacles like buildings, path loss due to attenuation and shadowing [2].

Second, for the wireless users, the transmission media is air as compared to the wiredcommunication where each transmitterreceiver pair is considered as an isolated point-to-point link.

MIMO system utilizes the feature of spatial diversity by using spatial antennas in a dense

multipath fading environment which are separated by some distance [3]. MIMO systems areimplemented to obtain diversity gain or capacity gain to avoid signal fading. The idea to

improve the link quality (BER) or data rate (bps) is the basic consideration behind the

development of MIMO systems by using multiple TX/RX antennas [4]. The core scheme of

MIMO is space-time coding (STC). The two main functions of STC: diversity & multiplexing.

The maximum performance needs tradeoffs between diversity and multiplexing.


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MIMO system employs various coding techniques for multiple antenna transmissions have

become one of the desirable means in order to obtain high data rates over wireless channels [5].

However, of considerable concern is the increased complexity incurred in the implementation

of such systems. MIMO antenna systems are used in recent wireless communications like

WiMAX, IEEE 802.11n and 3GPP LTE etc.

Fig. 1.1: MIMO System (2X2 MIMO Channel)

A. I. Sulyman [6] describes the performance of MIMO systems over nonlinear fading channels.

The effects ofantenna selection on its performance are also considered. The author has derived

expressions for the PWEP performance of space-time trellis coding nonlinear Rayleigh fading

channel. With the variation in the antenna selection at the receiver side, the performance

degradation due to nonlinear fading channel reduces.

The comparison of MIMO with conventional Single-Input Single-Output (SISO) technology

was discussed by S. G. Kim et. al [7]. The authors discussed that the MIMO system enhances

the link throughput and also improves the spectral efficiency. The authors analyzed the BER

performance of MIMO systems for M-PSK using ZF receiver over various fading channels in

the presence of practical channel estimation errors.

C. Wang [8] explains the approach to increase the capacity of MIMO systems by employing

spatial multiplexing. Maximum likelihood (ML) receiver achieves optimal performance

whereas the linear receivers like Zero-Forcing (ZF) receiver provide sub-optimal performance.

But Zero- Forcing receiver also offers significant reduction in computational complexity with

performance degradation in tolerable limits.

A simple transmit diversity scheme comprises of two transmit antennas and one receive

antenna was presented by X. Zhang et. al [9]. It provides the same spatial diversity order as that

can be achieved by maximal-ratio receiver combining (MRRC) which makes use of one

transmit antenna and two receive antennas.

A. Lozano et. al [10] compared the transmit diversity vs. spatial multiplexing in modern MIMO

systems. Antenna diversity is a preferred weapon used by mobile wireless systems against the

effect of fading. The prevalence of MIMO has opened the door for a much more effective useof antennas: spatial multiplexing.

The rich-scattering wireless channel is capable of enormous theoretical capacities if the

multipath is properly exploited as per the researches done in the field of Information theory. P.


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W. Wolniansky et. al [11], described an architecture of wireless communication known as V-

BLAST (Vertical Bell Laboratories Layered Space-Time) that has been implemented in real-

time environment.

An efficient implementation of space-time coding for the broadband wireless communications

is presented by R. S. Blum et. al [12]. The authors presented the improved performance of

MIMO-OFDM systems and diversity gains of a space time (ST) coding system through the typeof trellis codes used in non-linear fading channel environment. The developed

simulator for predicting the performance of a space time (ST) coded MIMO-OFDM system

under different trellis coding and channel conditions is demonstrated.

The performance analysis of the low-cost effective MIMO system that employs the spatial

multiplexing at the transmitter and zero-forcing processing at the receiver in multiuser

scheduling systems was discussed by C. Chen [13]. By incorporating the mathematical tool of

order statistics, the author derived the PDFs of effective sub channel output SNRs for a variety

of scheduling algorithms. These expressions are used to derive the closed-form formulas. The

closed-form expressions allow efficient numerical evaluations to characterize the capacity gain

of this suboptimal transmission strategy under a number of practical scheduling policies

requiring scalar or vector feedback. The results validate the elegant marriage of the zero-forcing

receiver and scheduling technique as an economical approach to achieve higher data rates for

next-generation wireless communications.

N. S. Kumar et. al [14], investigated about the three types of equalizer for MIMO wirelessreceivers. The authors discussed about a fixed antenna MIMO antenna configuration and

compare the performance with all the three types of equalizer based receiver namely ZF, ML,

and MMSE. BER performance of ML Equalizer is superior to zero forcing Equalizer and

Minimum Mean Square Equalizers. It is inferred that the ML equalizer is the best of the three

equalizers based on the mathematical modeling and the simulation results.

In this paper, the performance analysis of MIMO systems over AWGN and Rician channelsusing ZF receivers are presented. AWGN channel is a channel which has flat frequency

response. It is known as universal channel model used for analyzing modulation schemes. In

this, channel adds a white Gaussian noise to the signal passing through it. When there is line of

sight, direct path is normally the strongest component goes into deeper fade compared to the

multipath components. This kind of signal is approximated by Rician distribution.

II. BENEFITS OF MIMO SYSTEMSSpatial multiplexing

Spatial multiplexing which comprises of number of transmit-receive antenna pairs tend to

increase the transmission rate (or capacity) for the same bandwidth without any additional

power expenditure. The increase in the transmission rate is proportional to the number oftransmit-receive antenna pairs.

Interference reduction and avoidance

Multiple users which shares time and frequency resources result in interference in wirelessnetworks. Interference may be mitigated in MIMO systems by exploiting the spatial dimension


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to increase the separation between users. To improve the coverage and range of a wireless

network, there is need of interference reduction and avoidance.

Array gain

The coherent combining effect of multiple transmitting and receiving antennas tends to achievegood array gain at the receiver. This average increase in the SNR at the receiver requires

perfect channel knowledge either at the transmitter or receiver or both.

Diversity gain

Multipath fading is the most significant problem in wireless communications due to various

obstacles like building, scattering, reflection etc. In a fading channel, signal experiences fade

(i.e the fluctuation in the signal strength). The channel is in deep fade when there is a

significant drop in the signal power that gives rise to high BER. The diversity is used to so as tocombat fading as much as it can.

Table 1.1: Benefits of MIMO system

MIMO

TECHNIQUE

BENEFITS BEST CONDITIONS

SPATIAL

MULTIPLEXING

Increases the throughput of

the system

Best performance is achieved at low

velocity near to the base station (strong

signal)

TRANSMIT

DIVERSITY

Increases the range by

countering fading (less

possibility of errors)

usually at base station

Good when beam forming is not

appropriate

RECEIVE

DIVERSITY

Increases the range by

countering fading (less

possibility of errors)

usually at mobile station

Advantage over single antenna under all

conditions

BEAMFORMING Increases the range at base

station

Works best at relatively low velocity

when distance is extremely large (cell

edge).

III.MODULATION TECHNIQUEModulation is the process of superimposing a low frequency information signal over a high

frequency carrier signal so that its transmission is possible over a long distance. Modulation can

be analog and digital type. Digital modulation maps the digital information over analog carrier


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so as to transmit it over the channel. Every digital communication system has a modulator in

the transmitter side and a demodulator in the receiver side. Every transmitter has a modulator

that performs the task of modulation. Every r

eceiver has a demodulator to perform the inverse process of modulation, called demodulation,

so as to recover the transmitted digital information.

Fig. 1.2: Signal Space Diagram for 8-PSK

The M-ary PSK modulation yields circular constellation as the amplitude of the transmitted

signals remains constant as shown in Fig. 1.2.

The signal set for M-ary Phase-shift keying (M-PSK) can be represented as:

Xit 2EsTs cos 2 fc 2i1

M i 1,2, . . M &0 Ts (1.1)

where Es represents the signal energy per symbol, Ts represents the symbol duration and fcrepresents the carrier frequency.

This phase of the carrier changes for different possible values of M as follows:

2i 1/M i 1,2, . . M (1.2)

IV. CHANNELS USEDCommunication channels can be classified as fast and slow fading channels. In a fast channel,

the impulse response changes approximately at the symbol rate of the communication system,

whereas in a slow fading channel, it does not changes so frequently. Rather it stays unchanged

for several symbols. In this paper, the performance analysis of MIMO system is discussed over

the AWGN channel and Rician channel.

AWGN channel: It is a channel used for analyzing modulation schemes by adding awhite Gaussian noise to the signal passing through it. This channels amplitude frequency

response is flat and phase frequency response is linear for all frequencies. The modulated

signals pass through it without any amplitude loss and phase distortion. So in such a case,

fading does not exist but the only distortion that exists is introduced by the AWGN. The

received signal is simplified to


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rt xt nt (1.3)where n(t) represents the noise.

Rician channel: When there is line of sight, direct path is normally the strongestcomponent goes into deeper fade compared to the multipath components. This kind ofsignal is approximated by Rician distribution. As the dominating component run into more

fade the signal characteristic goes from Rician to Rayleigh distribution. The signal

characteristic goes from Rician to Rayleigh distribution as the dominating component run

into more fade in multi-path fading.

pr r2

e r2 A222

I Ar

for A 0, r 0 (1.4)

Where A denotes the peak amplitude (value) of the dominant signal and I o[.] is the

modified Bessel function of zero-order.

V. MIMO SYSTEM MODEL

Fig. 1.3: MIMO channel as n SISO sub-channels

The MIMO channel is represented in Fig. 1.3 with an antenna array with n t elements at the

transmitter and an antenna array with nr elements at the receiver is considered. The impulse

response of the channel is hij(,t) between the jth transmitter element and the ith receiver element.

The MIMO channel can then be described by the nr X nt H(,t) matrix:

(1.5)


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The matrix elements are complex numbers. These elements have dependency on the attenuation

and phase shift that the wireless channel introduces delay to the received signal reaching at

the receiver.

The input-output relation of the MIMO system can be expressed as follows:

yt H, t st ut (1.6)where denotes convolution, s(t) is a nt X 1 vector corresponding to the n t transmitted signals,

y(t) is a nr X 1 vector corresponding to the n r and u(t) is the additive white noise.

VI.ZERO FORCING EQUALIZERZero Forcing Equalizer was first proposed by Robert Lucky, is a linear receiver used incommunication systems. This equalizer inverts the frequency response of the channel to the

received signal so as to restore the signal before the channel. This receiver is called Zero

Forcing as it brings down the ISI to zero [5]. The frequency response of channel is assumed to

be F(f) and C(f) for the zero forcing equalizer, then this equalizer is constructed such that C(f) =1 / F(f). Thus this combination of channel and equalizer gives a flat frequency response and

linear phase.

The received signal can be represented by using the linear model as:

y Hx n (1.7)A 2x2 MIMO channel can be represented in matrix notation as follows:

y1y2 h1,1 h1,2

h2,1 h2,2 x1x2

n1n2

(1.8)

The signal received on the first receive antenna can be expressed as:

y1

h1,1x1 h1,2x2 n1 h1,1 h1,2 x1x2 n1 (1.9)The signal received on the second receive antenna can be expressed as:

y2

h2,1x1 h2,2x2 n2 h2,1 h2,2 x1x2 n2 (1.10)where

x1 and y1 is the transmitted and received symbol on the first antenna,

x2 andy2 is the transmitted and received symbol on the second antenna,h1,1 is the channel from 1st

transmit antenna to the 1st

receive antenna,h1,2 is the channel from 2

nd transmit antenna to the 1st receive antenna,

h2,1 is the channel from 1st transmit antenna to the 2nd receive antenna,

h2,2 is the channel from 2nd transmit antenna to the 2nd receive antenna,

and n1, n2 are the noise on 1st

and 2nd

receive antennas.


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VII. SIMULATED RESULTSIn this section, the BER analysis of MIMO system structure is done for M-PSK Modulation

techniques over AWGN and Rician fading channels using Space-Time Block Coding (STBC)structure. The BER analysis of MIMO system is done for M-PSK modulation for different

values of M. Here the value of M selected can be 32, 64, 128, 256, 512 and 1024 over both thefading channels.

(A)M-PSK over AWGN channel

(a) 32-PSK (b) 64-PSK

(c) 128-PSK (d) 256-PSK

0 5 10 15 20 25 3010

-3

10-2

10-1

100

signal to noise ratio

biterror

rate

SNR vs BER Plot of 32-PSK in AWGN Channel

No. of Rx = 1

No. of Rx = 2

0 5 10 15 20 25 3010

-3

10-2

10-1

100


biterror

rate


No. of Rx = 1

No. of Rx = 2

0 10 20 30 40 50 6010

-3

10-2

10-1

100


biterrorrate


No. of Rx = 1

No. of Rx = 2

0 10 20 30 40 50 6010

-3

10-2

10-1

100


biterrorrate


No. of Rx = 1

No. of Rx = 2


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(e) 256-PSK (f) 1024-PSK

Fig. 1.4: SNR vs BER plots using M-PSK over AWGN channel for different values of M

In Fig. 1.4 (a) (f), the SNR vs BER plots using M-PSK over AWGN channel for MIMO

system are presented for different values of M employing different antenna configurations. It

can be concluded from the graphs that with the increase in number of receiving antennas, the

BER keeps on decreasing due to space diversity in MIMO and thus the system proposed over

here provide better BER performance in comparison to the other antenna configurations.

(B) M-PSK over Rician channel

(a) 32-PSK (b) 64-PSK

0 10 20 30 40 50 6010

-3

10-2

10-1

100


biterrorrate


No. of Rx = 1

No. of Rx = 2

0 10 20 30 40 50 6010

-3

10-2

10-1

100


bit

errorrate


No. of Rx = 1

No. of Rx = 2

0 5 10 15 20 25 3010

-3

10-2

10-1

10

0


biterrorrate

SNR vs BER Plot of 32-PSK in Rician Channel

No. of Rx = 1

No. of Rx = 2

0 5 10 15 20 25 3010

-3

10-2

10-1

100


biterrorrate


No. of Rx = 1

No. of Rx = 2


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(c) 128-PSK (d) 256-PSK

(e) 512-PSK (f) 1024-PSK

Fig. 1.5: SNR vs BER plots using M-PSK over Rician channel for different values of M

The SNR vs BER plots using M-PSK over Rician channel for MIMO system are presented for

different values of M employing different antenna configurations are presented in Fig. 1.5 (a)

(f). From the graphs, it can be seen that if there is increase in the number of receiving

antennas in MIMO system then the BER keeps on decreasing due to space diversity. Thus this

system provides better BER performance as compared to the other antenna configurations.

VIII. CONCLUSIONIn this paper, SNR vs. BER plots for M-PSK over AWGN and Rician fading channels for

MIMO system employing different antenna configurations are presented. It can be concluded

that in MIMO system, the BER keeps on decreasing due to space diversity as we goes on

increasing the number of receiving antennas and the proposed system provide better BER

0 10 20 30 40 50 6010

-3

10-2

10-1

100


biterrorrate


No. of Rx = 1

No. of Rx = 2

0 10 20 30 40 50 6010

-3

10-2

10-1

100


biterrorrate


No. of Rx = 1

No. of Rx = 2

0 10 20 30 40 50 6010

-3

10-2

10-1

100


biterrorrate


No. of Rx = 1

No. of Rx = 2

0 10 20 30 40 50 6010

-3

10-2

10-1

100


biterrorrate


No. of Rx = 1

No. of Rx = 2


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performance. But BER is greater in Rician channel as compared to that of AWGN channel.

Also as we goes on increasing the value of M for M-PSK i.e the no. of constellation points in

the constellation diagram, the BER is also increasing. This increase in BER is due to the fact

that as increase the size of constellation diagram the spacing in between different constellation

point will keep on decreasing, which results in decreasing the width of decision region for eachconstellation point which in turn makes the detection of the signal corresponding to the

constellation point much tougher. Due to this fact the BER is increasing as we goes on

increasing the number of points in constellation diagram.

IX.REFERENCES[1] P. Sanghoi & L. Kansal, Analysis of WIMAX Physical layer Using Spatial Diversity, International

Journal of Computer Application, Vol. 44, Issue 5, 2012.

[2] L. Kansal, A. Kansal & K. Singh, BER Analysis of MIMO-OFDM Sytem Using OSTBC Code

Structure for M-PSK under Different fading Channels, International Journal of Scientific &

Engineering Research, Vol. 2, Issue 11, 2011.

[3] P. Sanghoi & L. Kansal, Analysis of WIMAX Physical layer Using Spatial Diversity under different

Fading Channels, International Journal of Computer Application, Vol. 44, Issue 20, 2012.

[4] S. Alamouti, A simple transmit diversity technique for wireless communications, IEEE Journal on

Selected Areas of Communication, Vol. 16, Issue 8, pp. 14511458, 1998.

[5] V. Tarokh, H. Jafarkhani & A. R. Calderbank, Spacetime block codes from orthogonal designs,

IEEE Transactions on Information Theory, Vol. 45, Issue 5, pp. 14561467, 1999.

[6] A. I. Sulyman, Performance of MIMO Systems With Antenna Selection Over Nonlinear Fading

Channels, IEEE Journal of Selected Topics in Signal Processing, Vol. 2, Issue 2, pp. 159-170,

2008.

[7] S. G. Kim, D. Yoon, Z. Xu & S. K. Park, Performance Analysis of the MIMO Zero-Forcing

Receiver over Continuous Flat Fading Channels, IEEE Journal of Selected Areas inCommunications, Vol. 20, Issue 7, pp. 324 327, 2009.

[8] C. Wang, On the Performance of the MIMO Zero-Forcing Receiver in the Presence of Channel

Estimation Error, IEEE Transactions on Wireless Communications, Vol. 6, Issue 3, pp. 805 810,

2007.

[9]X. Zhang, Z. Lv & W. Wang, Performance Analysis of Multiuser Diversity in MIMO Systems with

Antenna Selection, IEEE Transactions on Wireless Communications, Vol. 7, Issue 1, pp. 15-21,

2008.

[10] A. Lozano & N. Jindal, Transmit Diversity vs. Spatial Multiplexing in Modern MIMO Systems,

IEEE Transactions on Wireless Communications, Vol. 9, Issue 1, pp. 186-197, 2010.

[11] P. W. Wolniansky, G. J. Foschini, G. D. Golden & R. A. Valenzuela, V-Blast: An architecture for

realizing very high data rates over the rich-scattering channel, International Symposium on Signals,Systems and Electronics, pp. 295300, 1998.

[12] R. S. Blum, Y. Li, J. H. Winters & Q. Yan, Improved SpaceTime Coding for MIMO-OFDM

Wireless Communications, IEEE Transaction on Communications, Vol. 49, Issue 11, pp. 1873-

1878, 2001.

[13] C. Chen, Performance Analysis of Scheduling in Multiuser MIMO Systems with Zero-Forcing

Receivers, IEEE Journal of Selected Areas in Communications, Vol. 25, Issue 7, pp. 14351445,

2007.


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[14] N. S. Kumar, G. J. Foschini, G. D. Golden & R. A. Valenzuela, Bit Error Rate Performance

Analysis of ZF, ML and MMSE Equalizers for MIMO Wireless Communication Receiver,

European Journal of Scientific Research, Vol. 59, Issue 4, pp. 522532, 2011.

Authors

Navjot Kaur was born in Jalandhar. She received her B.Tech degree in

Electronics and Communication Engineering from Lovely Institute of

Technology, Phagwara, Punjab Technical University, Jalandhar, in 2008, and

presently pursuing M.Tech degree in Electronics and communication

engineering from Lovely Professional University, Phagwara, India. Her

research interests include MIMO systems and wireless systems.

Lavish Kansal was born in Bathinda. He received his B.Tech degree in

Electronics and Communication Engineering from PTU, Jalandhar in

2009 and M.E. degree in Electronics and Communication Engineering

from Thapar University, Patiala in 2011.He is working as AssistantProfessor in the department of Electronics and communication

Engineering, Lovely Professional University, Phagwara, India. He has

published 15 papers in International journals. His research area includes

Digital Signal Processing, Digital Communication & Wireless

Communication.

Performance Comparison of MIMO Systems over AWGN and Rician Channels with Zero Forcing Receivers

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